Finite Group DatabasebetaFinite Group Databasebeta| order | 4756 |
| automorphism | Aut(G) order 2663360 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1189 |
| derived, Hall | C29×C41 ⋊ C4 |
| Sylow | C41 ⋊ Dic29 |
| Sylow | C29 ⋊ Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1189 |
| commutator, hypocenter | C29×C41 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C29×C41 | C2 |
| LCS | G ▷ C29×C41 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 74 |
| transitive degree | μt(G) = 4756 |
Polycyclic presentation:
2,29,41,2|a^2=d,b^a=b^28,c^a=c^401192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1189, Dic3567, C5×Dic1189, … |
| maximal normal subgroup of | C3×Dic1189, C5×Dic1189, Dic1189⋊C5, … |
| maximal quotient of | C3×Dic1189, Dic3567, C5×Dic1189, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4756, 4);